Matrices & determinants worksheet with answers

Free printable Matrices & determinants worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
A =2−32−5

Find the determinant det A of the matrix A shown.

A = [2 −3; 2 −5]
det A =
2.Easy
A =−5−55−6

Find the determinant det A of the matrix A shown.

A = [−5 −5; 5 −6]
det A =
3.Medium
A =−4404B =2−1−2−1

Let C = AB for the matrices shown. Find the entry c21 (row 2, column 1).

A = [−4 4; 0 4]B = [2 −1; −2 −1]
c21 =
4.Medium
A =6−3−1−2B =20−5−5

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [6 −3; −1 −2]B = [2 0; −5 −5]
c11 =
5.Hard
A =3−38−7

Find the larger eigenvalue λ of the matrix A shown.

A = [3 −3; 8 −7]
λ =
6.Hard
A =−2−3−46b =108

Solve the system −2x − 3y = 10 and −4x + 6y = 8. Find x.

−2x − 3y = 10−4x + 6y = 8
x =

Answer key

  1. 1. det A = −4
  2. 2. det A = 55
  3. 3. c21 = −8
  4. 4. c11 = 27
  5. 5. λ = −1
  6. 6. x = −3.5

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